Raducanu was facing Switzerland’s Viktorija Golubic at a WTA 250 event in Nottingham when she felt as if something had been “thrown” from the side of her body.
But the US Open champion said she is looking for a return to the court later on the grass court swing.
“It was disappointing to leave this week with a side injury and unfortunately (I) will no longer be able to play in Birmingham,” Raducanu said in a statement released by the Lawn Tennis Association.
“I am looking forward to getting back on the match pitch soon to enjoy the rest of the grass season.”
Raducanu, 19, reached the fourth round of Wimbledon last year on his Grand Slam debut.
He then went on to win the US Open in September, but has struggled with form and fitness since his breakthrough last year and is currently without a coach.
On Tuesday, Raducanu said he had “no idea” if he would be able to compete at Wimbledon, which starts on June 27.